If you want to figure out how drywall should be hung, mud your own work. I
now hang everything so that the seem is the most accessible part. Plus
having one seem at chest height all around the room is a lot easier and
ecstatically pleasing.

Whew - usually drywall seams don't get me ecstatic, but to each his
own, I guess.
If this is just one corner you're working with, it seems like it
wouldn't be too hard to add another 2x4 (or even 2x2) screwed right on
to the existing one, which would give you plenty of wood for the screw
to "bite". Not sure if there would be any code issues with this, but
it seems like it would be a fairly straightforward fix.
Good luck,
Andy